Physics · Mechanical Properties Of Solids · NEET
In the sag formula δ = Wl³ / (4bd³Y), depth appears as d³ in the denominator but breadth appears only as b (power 1). So if you double the depth, sag falls to 1/8 of its value, but if you double the breadth, sag falls only to 1/2. Depth is far more powerful, so a good beam should be deep rather than wide.
A very deep, thin beam saves material but it can bend sideways and collapse under its own load. This sideways collapse is called buckling (NCERT Fig 8.7b). So you cannot make the beam too thin. The I-shape is the compromise: enough depth to resist bending, plus a wide top and bottom surface so it does not buckle.
The layers near the centre line (neutral axis) of a bending beam are hardly stretched or compressed, so they carry very little load. Material there adds weight and cost but almost no strength. Removing it leaves a thin vertical web, and the strong flanges stay at the top and bottom where stress is largest. This is why the section looks like the letter I.
No. A solid block of the same outer size would actually resist bending slightly more, but it would be much heavier and costlier. The point of the I-section is efficiency: it gives almost the same depth and load-bearing surface as a solid bar while using far less material, so it reduces weight and cost without a big loss of strength.
The two horizontal parts at the top and bottom are the flanges; they carry the tension and compression and provide the large load-bearing surface. The thin vertical part joining them is the web; it holds the flanges apart to keep the depth large. Flanges give strength, the web gives depth cheaply.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
For a bar of length l, breadth b, depth d and Young's modulus Y, loaded at the centre by weight W and supported near its ends, the sag (depression) is δ = Wl³ / (4bd³Y).
It gives a large depth and a large load-bearing surface to resist bending and buckling, while removing the weak middle material. This reduces weight and cost without sacrificing strength, which is ideal for long spans like bridges.
Yes. Since δ ∝ 1/Y, a larger Young's modulus means less bending for the same load. That is why steel, with a high Y, is preferred for beams.
Buckling is the sideways bending or collapse of a beam that is too deep and thin, especially when the load is not exactly centred. To avoid it, the beam is given wide flanges (the top and bottom of the I), which stop it from bending sideways.
NEET usually tests the reasoning and the sag formula δ = Wl³ / (4bd³Y): why depth beats breadth (d³ vs b), the role of Y, and why the middle is removed. Numerical questions apply the same formula to compare two beams.
